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For example, recent research shows that flow-based community detection methods can highlight spurious communities in sparse undirected and unweighted networks with missing links. Current Bayesian approaches developed to overcome this problem do not work for incomplete observations in weighted and directed networks that describe network flows. To overcome this gap, we extend the idea behind the Bayesian estimate of the map equation for unweighted and undirected networks to enable more robust community detection in weighted and directed networks. We derive an empirical Bayes estimate of the transitions rates that can incorporate metadata information and show how an efficient implementation in the community-detection method Infomap provides more reliable communities even with a significant fraction of data missing.<\/jats:p>","DOI":"10.1093\/comnet\/cnab044","type":"journal-article","created":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T11:08:52Z","timestamp":1635505732000},"source":"Crossref","is-referenced-by-count":14,"title":["Mapping flows on weighted and directed networks with incomplete observations"],"prefix":"10.1093","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0124-1909","authenticated-orcid":false,"given":"Jelena","family":"Smiljani\u0107","sequence":"first","affiliation":[{"name":"University of Belgrade Integrated Science Lab, Department of Physics, Ume\u00e5 University, SE-901 87 Ume\u00e5, Sweden and Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, , Pregrevica 118, 11080 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7881-2496","authenticated-orcid":false,"given":"Christopher","family":"Bl\u00f6cker","sequence":"additional","affiliation":[{"name":"Integrated Science Lab, Department of Physics, Ume\u00e5 University , SE-901 87 Ume\u00e5, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5420-0591","authenticated-orcid":false,"given":"Daniel","family":"Edler","sequence":"additional","affiliation":[{"name":"Department of Physics, Ume\u00e5 University, SE-901 87 Ume\u00e5, Sweden Integrated Science Lab, , Gothenburg Global Biodiversity Centre, Box 461, SE-405 30 Gothenburg, Sweden and Department of Biological and Environmental Sciences, University of Gothenburg, Carl Skottsbergs Gata 22B, Gothenburg 41319, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7181-9940","authenticated-orcid":false,"given":"Martin","family":"Rosvall","sequence":"additional","affiliation":[{"name":"Integrated Science Lab, Department of Physics, Ume\u00e5 University , SE-901 87 Ume\u00e5, Sweden"}]}],"member":"286","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"2022112115384919300_B1","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.1073\/pnas.0400087101","article-title":"The architecture of complex weighted networks","volume":"101","author":"Barrat,","year":"2004","journal-title":"Proc. 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